Parity-violating trispectrum from Chern-Simons gravity

Abstract

A potential source for parity violation in the Universe is inflation. The simplest inflationary models have two fields: the inflaton and graviton, and the lowest-order parity-violating coupling between them is dynamical Chern-Simons (dCS) gravity with a decay constant f. Here, we show that dCS imprints a parity-violating signal in primordial scalar perturbations. Specifically, we find that, after dCS amplifies one graviton helicity due to a tachyonic instability, the graviton-mediated correlation between two pairs of scalars develops a parity-odd component. This correlation, the primordial scalar trispectrum, is then transferred to the corresponding curvature correlator and thus is imprinted in both large-scale structure (LSS) and the cosmic microwave background (CMB). We find that the parity-odd piece has roughly the same amplitude as its parity-even counterpart, scaled linearly by the degree of gravitational circular polarization Πcirc ∼ √ε[h 2/(M Pl f)] ≤ 1, with ε the slow-roll parameter, H the inflationary Hubble scale, and the upper bound saturated for purely circularly-polarized gravitons. We also find that, in the collapsed limit, the ratio of the two trispectra contains direct information about the graviton's spin. In models beyond standard inflationary dCS, e.g. those with multiple scalar fields or superluminal scalar sound speed, there can be a large enhancement factor F ≳ 106 to the trispectrum. We find that an LSS survey that contains N modes linear modes would place an nσ constraint on Πcirc r of ∼ 0.04 (n/3)(106/F)(106/N modes)1/2 from the parity-odd galaxy trispectrum, for tensor-to-scalar ratio r. We also forecast for several spectroscopic and 21-cm surveys. This constraint implies that, for high-scale single-field inflation parameters, LSS can probe very large dCS decay constants f ≲ 4 × 109 GeV(3/n)(F/106)(N modes/106)1/2. Our result is the first example of a massless particle yielding a parity-odd scalar trispectrum through spin-exchange.